Evaluate the integrals in Exercises 53–58.
∫ from -π/2 to π/2 of cos(x) cos(7x) dx

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫ (r² + r + 1) e^r dr

Volume: Find the volume of the solid formed by revolving the region bounded by the graphs of y = sin x + sec x, y = 0, x = 0, and x = π/3 about the x-axis.

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ (sin⁻¹ x)² / √(1 - x²) dx

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ dx / (x √(x + 4))

In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.

∫₋₂¹ (1 / x⁴) dx

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ tan^(-1)(√y) dy